Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.5 SOLID–LIQUIDEQUILIBRIA 385

12.5.2 Solubility of a solid nonelectrolyte

Suppose we find that a solution containing solute B at a particular combination of temper-
ature, pressure, and composition can exist in transfer equilibrium with pure solid B at the
same temperature and pressure. This solution is said to besaturatedwith respect to the
solid. We can express thesolubilityof the solid in the solvent by the value of the mole frac-
tion, concentration, or molality of B in the saturated solution. We can also define solubility
as the maximum value of the solute mole fraction, concentration, or molality that can exist
in the solution without the possibility of spontaneous precipitation.
This section considers the solubility of a solid nonelectrolyte. For the solution process
B(s)!B(sln), the general expression for the thermodynamic equilibrium constant isKD
aB(sln)=aB(s).^8 The activity of the pure solid isaB(s)DB(s). Let us use a solute standard

state based on mole fraction; then the solute activity isaB(sln)Dx;B (^) x;BxB. From these
relations, the solubility expressed as a mole fraction is
xBD
B(s)K
x;B (^) x;B

(12.5.5)

If we measure the solubility at the standard pressure, the pressure factorsB(s) andx;B
are unity and the solubility is given by

xBD

K

(^) x;B

(12.5.6)

(solubility of solid B,pDp)

If the pressure is not exactly equal top, but is not very much greater, the values of the
pressure factors are close to unity and Eq.12.5.6is a good approximation.
We can find the standard molar enthalpy of solution of B from the temperature depen-
dence of the solubility. Combining Eqs.12.1.12and12.5.6, we obtain

Åsol,BHDRT^2

d ln.

x;BxB/

dT

(12.5.7)

(pDp)

The solubility may be small enough for us to be able to set the solute activity coefficient
equal to 1 , in which case Eq.12.5.7becomes

Åsol,BHDRT^2

d lnxB

dT

(12.5.8)

(pDp, (^) x;BD 1 )
If the solubilityxBincreases with increasing temperature,Åsol,BHmust be positive
and the solution process is endothermic. A decrease of solubility with increasing tem-
perature implies an exothermic solution process. These statements refer to a solid of low
solubility; see page 357 for a discussion of the general relation between the temperature
dependence of solubility and the sign of the molar differential enthalpy of solution at satu-
ration.
(^8) In this and other expressions for equilibrium constants in this chapter, activities will be assumed to be for
equilibrium states, although not indicated by the “eq” subscripts used in Chap. 11.